"We want to get an appreciation of the countryside."
In Germany this is surely possible by train. Two of Europe's most scenic train routes are in Germany, according to Eurail.com.
Then there's the Mosel Valley line between Koblenz and Bullay and the Neckar Valley line out of Heidelberg.
Trains also go to mountain towns like Berchtesgaden and Mittenwald. On Lake Constance, near the Swiss border, Lindau (island) is a popular train destination.
Germany has over 5,000 train stations. There are less than 40 cities in Germany with populations above 200,000. So obviously there are thousands of small cities and tiny towns that are served by train - including many towns on theme routes like the Fairy Tale Road, the Half-timbered Route, the German Castle Road, the German Wine Road, the Romantic Road - towns connected by asphalt but but possible by train too.
You will probably be interested in a German rail pass of some kind.
Note that the German Rail pass isn't just for Germany - it now includes some foreign destinations, including rail routes between Italy and Germany (see p.2.) Heading across the Alps by train is something you have time for and may be a more enjoyable way to get there than flying.
Here's a map showing Germany's extensive rail network.